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Question

Question 1

Part 1: If ∡JML =100°
, then which equation may be used to determine the value of x and the measure of the angles?

(1 point)
Responses

2x+(3x+30)=180
2 x plus open paren 3 x plus 30 close paren is equal to 180

2x+(3x+30) = 100
2x+(3x+30) = 100

2x+100=3x+30
2 x plus 100 is equal to 3 x plus 30
Question 2
(1 point)
Part 2: Determine the value of x and the measure of the angles.

x=


2x=
degrees

3x+30=
degrees

Answer 1

To solve for \(x\) and the measures of the angles, we consider the information given in the problem.

Since it states that the angle \( \angle JML = 100^\circ \), we can assume that angles \( 2x \) and \( 3x + 30^\circ \) are related to \( \angle JML \). Depending on the context of the angles (whether they are supplementary or complementary), the equations will differ.

Given the possible equations, let's go through them:

1. Equation: \( 2x + (3x + 30) = 180 \)

   • If \( 2x \) and \( 3x + 30 \) are supplementary angles, then this equation is correct, and we use it as:
     • \( 2x + 3x + 30 = 180 \)
     • Combining like terms gives:
     • \( 5x + 30 = 180 \)
     • Subtracting 30 from both sides:
     • \( 5x = 150 \)
     • Dividing by 5:
     • \( x = 30 \)

2. Now we can find the measures of the angles:

   • \( 2x = 2(30) = 60^\circ \)
   • \( 3x + 30 = 3(30) + 30 = 90 + 30 = 120^\circ \)

Now, let's summarize the results:

Values:

• \( x = 30 \)
• \( 2x = 60^\circ \)
• \( 3x + 30 = 120^\circ \)

Conclusion:

The correct equation to determine \(x\) and the angles is \( 2x + (3x + 30) = 180 \).

You can use these findings to fill in your answers.